Even Etiquetteer needs to check on what is Perfectly Proper or not, and one mystifyingly foggy aspect of etiquette has always been when and where a gentleman may wear his hat indoors. Movies are never really a reliable guide to How to Behave Properly, and yet there are so many old films in which men are seen wearing hats indoors (around poker tables, in hotel lobbies, etc.) that the practice must have had some wider acceptance. But one gag in Auntie Mame (1958) is about a man with his hands full needing to take his hat off in an elevator. What is the final word on this? To Etiquetteer's delight, the key to unlock the mystery was found in a gem of a book called Male Manners: The Young Man's Guide to: dating, good looks, making friends, getting into schools, clubs, activities, talking easily, job hunting, traveling, cars, and more, by Kay Corinth and Mary Sargent (1969). The key is whether or not a space is public or private. In someone's home or office, hats are removed when you enter. If it's an office building, and therefore public, your hat may remain on. If you're riding on a public bus, subway, or streetcar, it's Perfectly Proper to remain hatted. Gentlemen may leave their hats on in a public elevator (for instance, in an office building or a college campus), but not if it's an elevator for a residence (like one of those tall residential towers so fashionable in New York and elsewhere these days). This was Etiquetteer's big surprise, having always thought that a gentleman removed his hat in any elevator.
Two important exceptions exist where hats are always removed on entry: churches and restaurants. Of course this relates only to secular headgear.* Etiquetteer gets enraged when seeing hipsters or other men wearing those fashionable narrow-brimmed hats - or worse, baseball caps - inside churches. Stop it at once! Several years ago, Etiquetteer joined the audience of a New Year's Eve evening concert in a church and was put off by the usher barking "Hats off!" as soon as the door opened, not even giving Etiquetteer a chance to take it off first before being disciplined. Later, seeing the rest of the audience, Etiquetteer understood, but still felt rather abused.
To summarize, a gentleman may wear his hat inside in these places: public buildings (e.g. hotel lobbies, office buildings, and their elevators). A gentleman removes his hat when he enters these places: private homes (and their elevators), restaurants, churches and other houses of worship (unless religious headgear).
Etiquetteer is relieved that the "Bad Hair Day" excuse to remain hatted seems to have been capped. After all, if people think you can't manage your hair, do you think they'll think you can manage something more important, like your career?
* Once upon a time, it would not be necessary to state this, but with wider, and Perfectly Proper, acceptance of other cultures, it's important to specify.